Lecture2014Ch10Fa07

Lecture2014Ch10Fa07 - Chapter 10 Testing Claims Regarding a Parameter The other branch of statistical inference is concerned with testing

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Chapter 10 –Testing Claims Regarding a Parameter The other branch of statistical inference is concerned with testing hypotheses about the value of parameters. Defn : A hypothesis is a statement about the value of a population parameter. Defn : In a hypothesis test, the hypothesis which the researcher is attempting to prove is called the alternative (or research) hypothesis , denoted H a . The negation of the alternative hypothesis is called the null hypothesis , H 0 . The null hypothesis usually represents current belief about the value of the parameter. The researcher suspects that the null hypothesis is false, and wants to disprove it. Note : Hypotheses are tested in pairs (here the symbol μ 0 represents some specified number): If the null hypothesis is H 0 : μ = μ 0 , then the corresponding alternative hypothesis is H a : μ μ 0 . If the null hypothesis is H 0 : μ μ 0 , then the corresponding alternative hypothesis is H a : μ < μ 0 . If the null hypothesis is H 0 : μ μ 0 , then the corresponding alternative hypothesis is H a : μ > μ 0 . In each case, the alternative hypothesis is a strict inequality; the null hypothesis is not. The above hypothesis statements are written in terms of a population mean, μ . If we are testing hypotheses about a population proportion, p, or some other parameter, that parameter would appear instead of μ .
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: If the researcher wants to prove that the proportion, p, of the U.S. population who catch a cold between October 1 and March 31 is more than 40%, the two hypotheses would be stated as follows: H 0 : p 0.40 H a : p > 0.40 Example : If the researcher is in charge of quality control for the Pepsi-Cola Company, and wants to determine whether an assembly line at a plant which produces 12-oz. cans of Pepsi is working properly, the hypotheses would be stated as follows in terms of the mean amount of Pepsi in the cans: H 0 : μ = 12 oz. H a : μ 12 oz. Note : We cannot prove the null hypothesis; we may disprove it, or we may fail to disprove it. After taking a sample and conducting a test, we will either reject H 0 and believe H a , or we will fail to reject H 0 because of insufficient evidence against it. As Dr. Carl Sagan once said, “Absence of evidence is not evidence of absence.” There are four possibilities: 1) We reject the null hypothesis when the null hypothesis is, in fact, true. In this case, we make a Type I Error . 2) We reject the null hypothesis when the null hypothesis is, in fact, false. In this case, we make a correct decision. 3) We fail to reject the null hypothesis when the null hypothesis is, in fact, true. In this case, we make a correct decision. 4) We fail to reject the null hypothesis when the null hypothesis is, in fact, false. In this case, we make a Type II Error . We want to maximize the probability of making a correct decision,
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This note was uploaded on 07/28/2011 for the course STA 2014 taught by Professor Staff during the Fall '10 term at University of Florida.

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Lecture2014Ch10Fa07 - Chapter 10 Testing Claims Regarding a Parameter The other branch of statistical inference is concerned with testing

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